Beyond experimentally diagnosing transient entanglement dynamics in driven quantum materials, we anticipate the need for further theoretical developments. Here, we mainly discuss multipartite entanglement and quantum bounds in the spin basis. However, it is also important to characterize the entanglement depth of fermionic degrees of freedom via observables specific to indistinguishable particles. The intrinsic entanglement of a many-body state is a basis-independent property [1]}, i.e., it is invariant under a unitary transformation over all modes on the particle creation/annihilation operators. In a few-body system, the Slater rank number or fermionic concurrence [2]}, [3]}, [1]} can serve as basis-independent quantification of entanglement.
In a many-body material system, it is impractical to measure these quantities, but one can construct different witnesses to set tight bounds among various entangled states and to fit observables accessible by solid-state measurements. A promising witness for indistinguishable fermions is operators sensitive to paired states [5]}, constructed by at most two creation and two annihilation operators.
